In this axis, one of the research direction is focused on nonparametric and semi-parametric statistics for the design of optimal estimators (in the minimax sense, or from Oracle inequalities) for statistical inference problems in large dimension (deformable models in signal processing, covariance matrix estimation, inverse problems).
In this context, the first part focuses on the minimization of the Stein unbiased risk estimator (SURE) for variational models. A first theoretical difficulty is to design such estimators when the targeted functionals are non-smooth, non-convex or discontinuous. A second difficulty relates to the development of efficient algorithms for the calculation and minimization of the SURE when solutions of these models are themselves derived from an optimization algorithm. Finally, a last difficulty concerns the extension of the SURE to complex inference problems (ill-posed problems, non white Gaussian noise, etc.).
Another part of this axis concerns semi-parametric regression models when the regression function is estimated by a recursive Nadaraya-Watson type estimator. In this context, a “région Aquitaine” contract was obtained in 2014 for 3 years. It covers the development of new non-parametric estimation methods with applications in valvometry and environmental sciences.